In InfoPath you can break the form into views or sections. That allows the form tobe in more managable parts.
For what yoiu want add the controls to sections and then add a check box or make a button, remove the border and make the text underline. Have it set a field to true.
Then have conditional formatting on the section which collapse or hides a section.
So either make it wizard like where they next through the views or have collapsable sections.